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Simplifying 6a2 + -22a + -4 = 0 Reorder the terms: -4 + -22a + 6a2 = 0 Solving -4 + -22a + 6a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + -11a + 3a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -11a + 3a2)' equal to zero and attempt to solve: Simplifying -2 + -11a + 3a2 = 0 Solving -2 + -11a + 3a2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.6666666667 + -3.666666667a + a2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -3.666666667a + 0.6666666667 + a2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -3.666666667a + a2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -3.666666667a + a2 = 0 + 0.6666666667 -3.666666667a + a2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -3.666666667a + a2 = 0.6666666667 The a term is -3.666666667a. Take half its coefficient (-1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. -3.666666667a + 3.361111114 + a2 = 0.6666666667 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667a + a2 = 0.6666666667 + 3.361111114 Combine like terms: 0.6666666667 + 3.361111114 = 4.0277777807 3.361111114 + -3.666666667a + a2 = 4.0277777807 Factor a perfect square on the left side: (a + -1.833333334)(a + -1.833333334) = 4.0277777807 Calculate the square root of the right side: 2.006932431 Break this problem into two subproblems by setting (a + -1.833333334) equal to 2.006932431 and -2.006932431.Subproblem 1
a + -1.833333334 = 2.006932431 Simplifying a + -1.833333334 = 2.006932431 Reorder the terms: -1.833333334 + a = 2.006932431 Solving -1.833333334 + a = 2.006932431 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + a = 2.006932431 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + a = 2.006932431 + 1.833333334 a = 2.006932431 + 1.833333334 Combine like terms: 2.006932431 + 1.833333334 = 3.840265765 a = 3.840265765 Simplifying a = 3.840265765Subproblem 2
a + -1.833333334 = -2.006932431 Simplifying a + -1.833333334 = -2.006932431 Reorder the terms: -1.833333334 + a = -2.006932431 Solving -1.833333334 + a = -2.006932431 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + a = -2.006932431 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + a = -2.006932431 + 1.833333334 a = -2.006932431 + 1.833333334 Combine like terms: -2.006932431 + 1.833333334 = -0.173599097 a = -0.173599097 Simplifying a = -0.173599097Solution
The solution to the problem is based on the solutions from the subproblems. a = {3.840265765, -0.173599097}Solution
a = {3.840265765, -0.173599097}
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